All stacks and schemes considered are over \(\mathbb {C}\) . For a stack \(\mathcal {X}\) , denote by \(\text{Coh}\,(\mathcal {X})\)  the abelian category of sheaves on \(\mathcal {X}\) , by \(D^b(\mathcal {X})\)  the derived category of bounded complexes of coherent sheaves on \(\mathcal {X}\) , and by \(\text{Perf}\,(\mathcal {X})\)  the category of perfect complexes on \(\mathcal {X}\) . The categories considered are dg and we denote by \(\otimes \)  the product of dg categories [1]}.
